一种基于小波和矩阵型扩散的图像放大

提出了一种基于小波多分辨分析和矩阵型扩散的图像放大方法.该方法把原图像作为放大图像的小波低频子带,初始高频置零小波重构,用矩阵型扩散方程处理后小波分解,得到估计的高频再与原图像重构.在扩散中取矩阵型扩散的扩散系数,选择其特征根,使扩散在垂直于边缘方向梯度较大时为逆扩散以锐化边缘,而沿边缘方向为正向扩散以增强边缘;同时提出了放大图像与原图像的一种相似性标准.该方法在放大图像的同时既去除了噪音又有效保持了边缘.数值实验结果证实,此方法为一个有效地图像放大方法.     

A note on a class of solitary-like solutions of the Tzitzéica equation generated by a similarity reduction

In this paper, new class of solutions of the Tzitzéica equation are derived by using the classical Lie symmetry analysis. The important aspect of this paper however is the fact that the analysis results in a new class of solitary-like solutions, the so-called cusp-solitary solutions.

This special type of solutions are not found in the current literature and represents a necessary contribution for the whole solution manifold. The studied equation was originally found in the field of geometry, otherwise the Tzitzéica equation takes place in many branches of non-linear sciences. Therefore, explicit class of solutions connected by a physical meaning are of great importance. The analysis is restricted to the case of traveling waves represented by a similarity variable describing any wave propagation. A complete characterization of the group properties is given. The classical Lie point symmetries are derived and algebraic properties are determined. Similarity solutions and transformations are given in a most general form and have been derived for the first time in terms of Jacobian elliptic functions. It is worth to mention that the application of known powerful algebraic methods (e.g. special function transform methods) are not appropriate to study the solution manifold. Hence, the present paper is therefore suitable to create a deeper insight into the solution manifold with respect to the traveling wave picture.     

An improved lesion detection approach based on similarity measurement between fuzzy intensity segmentation and spatial probability maps

The application of automatic segmentation methods in lesion detection is desirable. However, such methods are restricted by intensity similarities between lesioned and healthy brain tissue. Using multi-spectral magnetic resonance imaging (MRI) modalities may overcome this problem but it is not always practicable. In this article, a lesion detection approach requiring a single MRI modality is presented, which is an improved method based on a recent publication. This new method assumes that a low similarity should be found in the regions of lesions when the likeness between an intensity based fuzzy segmentation and a location based tissue probabilities is measured. The usage of a normalized similarity measurement enables the current method to fine-tune the threshold for lesion detection, thus maximizing the possibility of reaching high detection accuracy. Importantly, an extra cleaning step is included in the current approach which removes enlarged ventricles from detected lesions. The performance investigation using simulated lesions demonstrated that not only the majority of lesions were well detected but also normal tissues were identified effectively. Tests on images acquired in stroke patients further confirmed the strength of the method in lesion detection. When compared with the previous version, the current approach showed a higher sensitivity in detecting small lesions and had less false positives around the ventricle and the edge of the brain.     

Mapping quantum many-body system to decoupled harmonic oscillators: General discussions and examples

We present a class of quantum systems that can be mapped to decoupled harmonic oscillators through appropriate similarity transformations. We will take advantage of these similarity transformations to discover hidden ladder operators, such that the eigenstates of the system can be constructed like those of harmonic oscillator. We also provide five systems belonging to this family as examples.     

Shock wave driven out by a piston in a mixture of a non-ideal gas and small solid particles under the influence of the gravitation field with monochromatic radiation

Similarity solutions for a spherical shock wave in a mixture of small solid particles of micro size and a non-ideal gas are discussed under the influence of the gravitational field with monochromatic radiation. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Due to the central mass ($\overline{m}$) at the origin (Roche model), the medium is considered to be under the influence of the gravitational field. In comparison to the attraction of the central mass at the origin, the gravitational effect of the mixture itself is neglected. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. The effect of the parameter of non-idealness of the gas $\overline{b}$, the mass concentration of solid particles in the mixture μ_p, the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ are obtained. It is shown that due to an increase in the gravitational parameter the compressibility of the medium at any point in the flow field behind the shock front decrease and the flow variables velocity, pressure, radiation flux and shock strength are increased. Also, an increase in the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ has the same effect on the shock strength and the reverse effect on the compressibility. The non-idealness of the gas causes a decrease in the shock strength and widens the disturbed region between the piston and the shock.     

Super-spherical cumulation: shock collapse which is more intense than the spherical one

A shock wave implosion in an axisymmetric chamber with a convex bounding wall is studied experimentally, analytically and numerically. The converging shock front area in this geometry shrinks quickly as the shock wave approaches the center point. The analytical theory predicts that the corresponding rate of post-shock pressure and density increase in this case exceeds essentially that achieved in the classical cylindrical or spherical shock implosions, hence, the phenomenon is referred to as “super-spherical cumulation”. The experiments confirm higher intensity of the super-spherical implosion compared with the cylindrical one, both driven by identical high-current pulsed electric discharges. The converging shock stability is analyzed in the framework of the CCW theory. The numerical results obtained using a locally-adaptive unstructured grid technique agree well with the theoretical predictions of the converging shock wave intensity. Received 28 January 1998 / Accepted 6 November 1998     

模糊粗糙集的包含度和相似度

证明了包含度和相似度的几个性质,定义了模糊粗糙集的包含度和相似度。所证性质可用于生成模糊粗糙集的包含度和相似度。